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On pexiderized Jensen-Hosszú functional equation on the unit interval. (English) Zbl 1306.39020
Summary: We solve the functional equation of the form \[ 2f\biggl(\frac{x+y}{2}\biggl)=g(x+y-xy)+h(xy) \] in the class of real functions defined on the unit interval \([0,1]\). We prove that it is not stable, but if two functions from the triple \(\{f,g,h\}\) coincides the analogue equation is stable in the Hyers-Ulam sense.

39B82 Stability, separation, extension, and related topics for functional equations
Full Text: DOI
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